Question

How do you graph `y=5/4x+5`?

Answer 1

`"see explanation"`

Explanation:

`"to graph the line we only require 2 points"`

`"choose values of x and evaluate for y in the equation"`

`x=0toy=0+5=5`

`x=4toy=(5/4xx4)+5=5+5=10`

`"plot the points "(0,5)" and "(4,10)`

`"and draw a straight line through them"`
graph{(y-5/4x-5)((x-0)^2+(y-5)^2-0.04)((x-4)^2+(y-10)^2-0.04)=0 [-20, 20, -10, 10]}

Answer 2

x-intercept is `color(blue)[(-4, 0)`

y-intercept is `color(blue)[(0, 5)`

Graph is available as a part of this solution.

Explanation:

We are given a linear equation `color(red)(y=5/4x+5)`

Please note that it is in Slope-Intercept Form

To draw a graph, we will follow the procedure as shown below:

`color(green)(Step.1`

We will find the x-intercept and the y-intercept

To find the x-intercept, let `color(red)(y = 0)` in our linear equation:

`color(red)(y=5/4x+5)`

We get,

`0=5/4x+5`

Add `color(blue)(-5)` to both sides:

`0 + color(blue)[(-5)]=5/4x+5 + color(blue)(-5)`

`0 + color(blue)[(-5)]=5/4x+cancel 5 + color(blue)((-cancel 5)`

`rArr 5/4x = -5`

Multiply both sides by `color(blue)(4/5)`

`rArr [5/4]x*color(blue)(4/5) = -5*color(blue)(4/5)`

`rArr [cancel 5/ cancel 4]x*color(blue)(cancel 4/cancel 5) = -5*color(blue)(4/5)`

`rArr x = -5*(4/5)`

`rArr x = -20/5`

`rArr color(blue)(x = -4)`

Hence, the point is `color(blue)[(-4, 0)`

To find the y-intercept, let `color(red)(x = 0)` in our linear equation:

`color(red)(y=5/4x+5)`

We get,

`y=5/4*(0)+5`

`color(blue)(y=5)`

Hence, the point is `color(blue)[(0, 5)`

`color(green)(Step.2`

Plot the Points `color(blue)[(-4, 0) and (0, 5)` on a Graph Paper

Use a straightedge and draw a straight line joining the points.

Please refer to the graph below:

graph{y=5/4x+5 [-20, 20, -10.42, 10.42]}